Pertentage Problems and Solutions

Q-1) What is percentage value of 7/20?
Solution:
7/20 = (7/20 × 100)% = 35%

Q-2) Convert percentage in fraction
(1) 16 % = 16/100 = 4*4/25*4 = 4/25
(2) 48 % = 48/100 = 12*4/25*4 = 12/25
(3) 5 % = 5/100 = 5/20*5 = 1/20
(4) 25 % = 25/100 = 25/25*4 = 1/4
(5) 115 % = 115/100 = 23*5/20*5 = 23/20
(6) 1 % = 1/100

Q-3)Find 30 % of 90
Solution:
30 % of 90
= 30/100 × 90
= (30 × 90)/100
= 2700/100
= 27

Q-4) In a class of 70 students, 30% are girls. Find total girls and total boys in the class?
Solution:
Total girls in the class: 
= 30 % of 70
= 30/100 × 70
= 2100/100 
= 21

Total boys in the class: 
= Total students in class - Number of girls
= 70– 21
= 49

Q-5) Raj scored 444 marks out of 500 marks and his elder brother Dharm scored 580 marks out of 600 marks. Who scored better percentage?
Solution:
Percentage of marks scored by Raj 
= (444/500 × 100) %
= (44400/500) %
= (444/5) %
= 88.8 %

Percentage of marks scored by Dharm 
= (580/600 × 100) %
= (58000/600) %
= (580/6) %
= 96.6 %
Hence, the percentage marks scored by Dharm is better.

Q-6) Two friends Raj & Rose had some chocolates each. One of them had 15 chocolates more than the other. The chocolates with Raj was 60% of the total chocolates with them. How many chocolates did each have?

Solution: 
Lets assume the chocolates are (x + 15) and x.
Therefore, 
x + 15 = 60/100 (x + 15 + x)
(x + 15) = 3/5 (2x + 15)
5x + 75 = 6x + 45
x = 30
So, the chocolates with two friends are 45 and 30.

Q-7) A fruit seller had some mangoes. He sells 30% mangoes and still has 140 mangoes. Originally, he had how many mangoes ?
  Solution:
Lets assume originally he had x mangoes.
Then, (100 - 30)% of x = 140.
70/100 x = 140
x = (140 x 100)/70 = 200.
So, originally he had 200 mangoes  

Q-8)  A student by mistake multiplied a number by 2/5 instead of 5/2. 
What is the error in percentage calculation?

Solution:
Let the number be 100
2/5 of 100 is 40 
while 5/2 of 100 is 250
So, the difference is 210 (i.e 250-40) on a base of 250. 
Now, percentage difference is 
(210/250) *100 = 84%
So, percentage error is 84%

Q-9)  Three candidates, Raj, Ajay & Amar contested an election and received 1800, 3300 and votes 3900 respectively. What percent of the total votes did Raj get??

Solution:
Total no. of votes = (1800 + 3300 + 3900) = 9000.
Required percentage = (1800/9000 * 100)% = 20%. 
So, percentage of votes Raj has is 20%

Q-10) A showowner bought 600 bananas and 400 mangoes. He found 15% of bananas and 8% of mangoes were rotten. Find the percentage of fruits in good condition.

Solution:
Total fruits showowner bought = 600 + 400 = 1000
Number of rotten bananas = 15% of 600 
= 15/100 × 600
= 9000/100
= 90
Number of rotten mangoes = 8% of 400
= 8/100 × 400
= 3200/100
= 32
So, total rotten fruits = 90 + 32 = 122
So, fruits in good condition = 1000 - 122 = 878
So, fruits in good condition = (878/1000 × 100)%
= (87800/1000)%
= 87.8%

Q-11) raj had $2200 left after spending 20% of the money he had for shopping. 
How much total money did he take with him?

Solution:
Lets assume Raj had taken total money M
Money he spend = 20% of M
=20/100*M

Money Left with Raj = M - (20/100*M)
Actual money left =  $2200
so, $2200 = M - (20/100*M)
$2200 = M-2M/10
$2200 = (10M-2M)/10
$2200 = 8M/10
($2200 * 10)/8 = M
M=($2200 * 10)/8 
M=$2750
Total money he had = $2750